which collapses into \(R_{\mathrm {part.}}\)  for large enough invariant masses \(M\)  such that asymptotic freedom is reached.
The perturbative expression can be used to estimate the lowest order \(q\bar{q}\)  annihilation rates in IMR (see [1]}).
However, as already discussed above, the calculations using hard-thermal-loop corrections provide rates larger by one order of magnitude than the estimates obtained with one-loop approximation [2]}. Similar results for dilepton radiation rates have also been obtained in recent coarse grained [3]}, [4]} and by fireball models [5]}, [6]} using lattice QCD results (for \(\mu _b=0\) ) for the vector spectral functions above \(T_{\mathrm {pc}}\) .
One should note that effects of in-medium hadronic spectral function, as we will discuss them below, are suppressed in this mass region by \(T^2/M^2\)  [5]}.
